为了证明这个定理，我们假定这个圆G能按上述方式画在一个球面上。

To prove the theorem we shall suppose that the graph G is drawn on a sphere as described above.

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如果向量场在原点处没有定义，但其他地方有定义，是不能用Stokes定理的，但还是有办法的，可以对半球面用的。

If your vector field is not defined at the origin but defined everywhere else you cannot use this guy, but maybe you can still use, say, the half-sphere, for example.

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本文给出了关于全挠率的一个著名定理：“球面闭曲线的全挠率为零”一个新的简单证法，并且给出了这个定理的两个推广定理。

A new and simple proving method on the famous theorem of total torsion, "the total torsion of closed spherical curve is zero", and two generalized theorems for the. theorem are presented in the paper.

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